Since you posted that there are USB ports on the front of this computer, I'm guessing that this is a desktop?
Let's see if the power switch is working properly.
If you have a multimeter you can set it to the Ohms scale to test if the power switch is functioning. You will need to turn off the computer and unplug it from the wall receptacle.
Before you touch anything inside the case touch the bare metal of the case to discharge any static electricity in your system. Electrostatic discharges can kill board components.
If you open the side panel of the case you will see the motherboard. You will see a header similar to the one in the image below.
Each connector on this header will be labeled, the power switch is usually labeled PW. It will have two wires in the connector.
If you remove this connector you can take a paper clip which you have cut into two straight pieces and insert these in the connector. Then you need to set the meter to the Ohm scale and place the two lead against the two paper clip parts (wires). Now press the power button and there should be a change in the meter reading. If this is an analog meter it will have a needle which should move. If it is a digital meter, the numbers will change. If nothing happens with the meter set properly and placed properly against the two wires, the switch is bad.
If you do not have a multimeter there is another way to test to see if there is a problem with the switch. For this you will need to have the computer plugged into the wall receptacle.
Locate the power switch connector and remove it from the header pins. Take a small slot type screw driver and very briefly place it so that it touches the two headers at the same time. This should start the computer.
If the switch is good you will need to determine if there is a problem with the motherboard. To do this, use the instructions below.
The purpose of this procedure is to bypass the motherboard to test the PSU.
When a computer begins the boot process the motherboard initiates the start up of the PSU. Because of this it is difficult to determine whether the problem is with the motherboard or the PSU when a computer shows no signs of starting up. The purpose of the procedure is to determine if the problem is with the motherboard or the PSU. For safety purposes please follow the instructions step by step.
Caution: Since it will be necessary for your computer to be on during this procedure, you need to be aware that you will be working with live 12Volt DC potentials, which if handled improperly may lead to electrical shock. The risks are minimal, but are there nevertheless. If you are uncomfortable doing this procedure I would suggest you not try this. Anyone using this tutorial will be doing so at their own risk.
There are electronic components inside the case that are very susceptible to electrostatic discharges. To protect your computer, touch the metal of the case to discharge yourself of any electrostatic charge before touching any of the components inside.
Shut down your computer, then unplug the power cable from the rear of the computer. To reduce the possibility of any shock press and hold the power button for thirty seconds to discharge any capacitors still holding a charge.
The connector of the PSU which connects to the motherboard is readily recognizable by the large number of wires in the bundle. To disconnect it you will need to press on the plastic clip to disengage it and then pull the connector up and away from the motherboard. Please take notice of the location of the locking tab and the notch on the socket of the motherboard, this will only connect one way as it is keyed. This wire bundle will have a memory of the way it has been installed and will want to bend back that direction, you may have to play around with it to find a position that the connector will stay in the same position while you run the test.
From the top left to right the pins are 13-24, the bottom from left to right are 1-12.
Below are the pinouts for the 20 and 24 pin ATX form factor connectors.
Please notice that there are PSUs with 24 pin and 20 pin connectors, the location of the green wire in the 24 pin connector is #16, and the green wire in the 20 pin connector is #14. If you look at the connector with socket side facing you and the clip on the top the number one pin will be on the bottom left corner. This makes the pin out for the 24 pin connector from left to right 13-24 on top, and 1-12 on the bottom. The pin out for the 20 pin connector from left to right is 11-20 on top , and 1-10 on the bottom. If you look at the connectors you notice that these are sockets that fit over the pins on the motherboard where the PSU cable attaches, this is where you will place the jumper. For a jumper you will need a piece of solid wire about the size of a paper clip (20-22 awg), preferably a wire with insulation. It will need to be large enough to fit firmly into the socket so that it will not need to be held in place while testing. You are at risk of electrical shock if you are holding the jumper when you power up the PSU. Insert one end of the jumper into the socket of the Green wire, and insert the other end into the socket of any Black wire.
Once the jumper is in place plug the cord back in. If the PSU is working properly the case fans, optical drives, hdds, and LEDs should power up and remain on.
To reconnect the 20/4 pin connector unplug the power cord, remove the jumper, and reconnect the connector. Take a moment at this time to make sure that nothing has been dislodged inside the case.